Answer:
Step-by-step explanation:
[tex]\frac{x+6}{x^2(x^2+2)} =\frac{A}{x} +\frac{B}{x^2} +\frac{Cx+D}{x^2+2} \\x+6=Ax(x^2+2)+B(x^2+2)+(Cx+D)x^2\\equating~co-efficients ~of~same~powers~of~x\\0=A+C (of~x^3)\\0=B+D (of~x^2)\\1=2A (of~x)\\A=1/2\\6=2B (constant~term)\\B=6/2=3\\C=-A=-1/2\\D=-B=-3\\\frac{x+6}{x^2(x^2+2)} =\frac{1}{2x} +\frac{-3}{x^2} +\frac{-\frac{1}{2} x-3}{x^2+2}[/tex]
What is (f- g)(x)?
f(x)=x^4-x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x)
A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
Step-by-step explanation:
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
To find (f-g)(x):
The operations on functions are as easy as the operations on numbers or polynomials.
We have to subtract the functions to find the above mentioned operation.
(f-g) (x)= f(x)-g(x)
= (x¹ - x² +9)-(x³ + 3x² + 12)
The minus will change the signs of function g.
gage stocks two ponds with bass and blue hill. he stocks pond a with 60 fish and pond b with 300 fish. gage stocks pond b with twice the amount of bass and six times the amount of bluegills as pond a. how many bass and bluegills does gage stock in pond w
Finally, we can use the earlier equations to find the number of bass and bluegills in pond B:
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
What is a math equation, exactly?In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.
Let's denote the number of bass in pond A as "x" and the number of bluegills in pond A as "y".
According to the problem, Gage stocks pond B with twice the amount of bass as pond A, so the number of bass in pond B is 2x. He also stocks pond B with six times the amount of bluegills as pond A, so the number of bluegills in pond B is 6y.
We know that Gage stocks pond A with a total of 60 fish, so:
x + y = 60
We also know that Gage stocks pond B with a total of 300 fish, so:
2x + 6y = 300
x + 3y = 150
Now we have two equations:
x + y = 60
x + 3y = 150
We can solve for x in the first equation:
x = 60 - y
Substitute this expression for x into the second equation:
(60 - y) + 3y = 150
2y = 90
y = 45
Now that we know that pond A has 45 bluegills, we can use the equation x + y = 60 to find that pond A has 15 bass (since 45 + 15 = 60).
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
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Select ALL of the solutions of the following system of linear inequalities below.
The solutions of the system of inequalities are:
(0, 3)
(6, 2)
How to find the solutions of the system?Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).
And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.
Then the points that are solutions are:
(0, 3)
(6, 2)
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The way entertainment is sold and viewed has changed drastically in the past decade. In the year
2011, there were 6.1 billion DVDs sold worldwide. In the year 2021, the number had declined to
1.2 billion.
a. What is the average rate of change in DVD sales during this period?
b. Using the numbers in 2011 as an initial value, write a linear model that models the
number of DVD sales worldwide. Make sure to define the variables.
c. If the rate stays the same, predict the number of DVD sales in the
year 2023.
Answer:
Step-by-step explanation:
a. The average rate of change in DVD sales during this period can be calculated as:
average rate of change = (change in DVDs sold) / (change in years)
We are given that in 2011, 6.1 billion DVDs were sold, and in 2021, 1.2 billion DVDs were sold. The change in DVDs sold is:
change in DVDs sold = 1.2 billion - 6.1 billion = -4.9 billion
The change in years is:
change in years = 2021 - 2011 = 10
So the average rate of change in DVD sales during this period is:
average rate of change = (-4.9 billion) / 10 = -0.49 billion DVDs per year
Therefore, DVD sales declined by an average of 0.49 billion per year during this period.
b. Using the numbers in 2011 as an initial value, we can write a linear model that models the number of DVD sales worldwide as:
DVD sales = -0.49(t - 2011) + 6.1
where t is the year and DVD sales are measured in billions.
c. If the rate stays the same, we can predict the number of DVD sales in the year 2023 by substituting t = 2023 into the linear model and solving for DVD sales:
DVD sales = -0.49(2023 - 2011) + 6.1 ≈ 0.5 billion DVDs
Therefore, if the rate of decline in DVD sales stays the same, we can predict that there will be about 0.5 billion DVDs sold worldwide in 2023.
Lee Ann bought 2 cartons of yogurt. She ate 1/8 of a carton of yogurt each day.
How many days did it take Lee Ann to eat all of the yogurt in the 2 cartons?
Answer:
B 16
Step-by-step explanation:
It will take 8 days to eat one carton so 2 cartons will be 16 days.
please help, i inserted the photo below and i need the answer asap
By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.
How to determine the length of a missing side in a system of similar triangles
Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:
BD / AD = CD / BD
BD² = AD · CD
BD = √(AD · CD)
And the length of the line segment AB can be determined by Pythagorean theorem:
AB = √(BD² + AD²)
If we know that AD = 4 and CD = 12, then the length of the line segment AB is:
BD = √(4 · 12)
BD = √48
BD = 4√3
AB = √[(4√3)² + 4²]
AB = 8
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i need help with this
The supplied statement states that the candle would reach a height of 14.85 cm after 24 hours.
What does the word "height" mean?The terms "altitude" and "elevation" refer to the vertical distance between something's top and bottom or its base and it's something above it. Height is used to describe everything that may be measured vertically, high or low.
Let Y = height.
let X equal time
Y = mX + b, where the slope of m & b is the y-intercept, denotes the linear relationship between height and time.
We can determine the slope using the information provided (13, 15.4) and (29, 6.5)
Slope = (y2 - y1) / (x2 - x1) = (6.5 - 15.4) / (29 - 13) = -8.9 / 16 = -0.55
This indicates that the candle is losing height at a rate of 0.55 cm each hour.
As the first grid cell of 24 hours comes 13 hours afterwards, (13, 15.4), the height will go down by 13 * (-0.55) = -7.15 cm in the 13 hours between hour 13 and hour 24.
Hence, the candle's height 24 hours later = 15.4 - 0.55 = 14.85 centimeters
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To indirectly measure the distance across a lake, Mia makes use of a couple
landmarks at points Vand W. She measures UX, XV, and XY as marked. Find
the distance across the lake (VW), rounding your answer to the nearest hundredth
of a meter.
W
70 m
120.25 m
130 m
U
The distance across the lake VW is 185m.
Define the term similar triangle?Triangles that are similar but not necessarily the same size are called similar triangles. This indicates that their sides are proportional and that their angles are the same.
We can see there are two similar triangles with interior parallel line.
So, apply the Side Angle Side (SAS) rule for ΔUVW ≈ ΔUXY;
⇒ [tex]\frac{VW}{XY} = \frac{UV}{UX}[/tex]
⇒ [tex]\frac{VW}{120.25}=\frac{(130+70)}{130}[/tex]
Cross multiply both sides,
⇒ VW = [tex]\frac{200}{130}*120.25[/tex]
⇒ VW = 185 m
Therefore, the value of VW is 185m.
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Find the area of the blue-shaded region. Please help I need it asap. The answer is 20.0m squared I cannot figure out the work for it
The area of the blue-shaded region is 19.95 m²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,
Using the Pythagoras theorem,
15.5² = 14²+w² [width]
w² = 240.25-196
w² = 44.25
w = 6.65
Therefore, the width of the rectangle is 6.65 m
That mean, the height of the parallelogram is 6.65 m,
The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,
Area of the remaining region = 14×6.65-11×6.65
= 6.65(14-11) = 6.65×3
= 19.95 m²
Hence, the area of the blue-shaded region is 19.95 m²
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1. we have to buy flat bar length=1ft.that is 2pesos per cm.how much money we need to buy for that flat bar?
Answer:
The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:
There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:
2 * 30.48 = 60.96
It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.
Step-by-step explanation:
Hope it helps! =D
There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = .4, P(F) = .2 and P(E intersect F) = .15.
(a) What is the probability that the individual must stop at at least one light; that is, what is the probability of the event P(E union F)?
The probability that the individual must stop at at least one light that is 0.45.
What is Probability?Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.
Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -
P(E) = 0.4P(F) = 0.2 P(E ∩ F) = 0.15.We can write -
P{E ∪ F} = P{E} + P{F} - P{E ∩ F}
P{E ∪ F} = 0.4 + 0.2 - 0.15
P{E ∪ F} = 0.6 - 0.15
P{E ∪ F} = 0.45
Therefore, the probability that the individual must stop at at least one light that is 0.45.
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Find the original price of a fitness watch that is $105 after 30% discount
18. If the points A and B are 16 m apart and points A and Care 22 m apart, find the distance between B and C
After doing some thinking, I believe it's 6 m.
Model Real Life B.E.S.T. Test Prep Wetlands make up about of the area of Florida. Select all the expressions that represent this fraction. A three-tenths (B) ten-thirds c) 3 tens D 10 thirds E 3 tenths Almost of the sp in Florida's wetlanc rare and endange
As wetlands make up about 31% of the area of Florida, the expressions that represent this fraction is:
three-tenths3 tenthsWhat percentage of the area of Florida does Wetlands make up?Florida wetlands generally include swamps, marshes, bayheads, bogs, cypress domes and strands, sloughs, wet prairies, riverine swamps and marshes, hydric seepage slopes, tidal marshes etc. According to the United States Environmental Protection Agency (EPA), wetlands cover approximately 31% of the total land area of the state of Florida.
Total land mass of Florida is: 170,312 Km². The landmass of Wetland areas is: 31% * 170,312 Km² = 52796.72Km²
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There are 2.5 times the amount of girls in a class than boys. If there are 35 students in the class, calculate the number of girls in the class.
Answer:
25
Step-by-step explanation:
Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:
number of girls = 2.5 * number of boys
We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:
x + 2.5x = 35
Simplifying the above equation, we get:
3.5x = 35
Dividing both sides by 3.5, we get:
x = 10
This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:
number of girls = 2.5 * number of boys
number of girls = 2.5 * 10 = 25
Therefore, there are 25 girls in the class.
6/cm
4 cm
Find the value of x.
X
x = [?]
Applying the secant-tangent theorem, the value of x is calculated as: x = 5.
What is the Secant-Tangent Theorem?The secant-tangent theorem states that if there is a point outside of a circle and we draw a tangent line and a secant line from that point to the circle, then the length of the tangent line squared is equal to the length of the secant line multiplied by the length of the part of the secant line that is outside the circle.
Therefore, applying the secant-tangent theorem:
4 * (x + 4) = 6²
4x + 16 = 36
4x = 36 - 16
4x = 20
4x/4 = 20/4
x = 5
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Without multiplying, drag the correct symbol into the box below.
<>=
1
3
4
×
3
1
4
1
3
4
The correct symbol for the given equation in the blank is the sign of non-equal to that ≠.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
here, we have,
Let's solve the given equation,
3 (3+4) = 3³
3 (7) = 27
21 ≠ 27.
Therefore, it shows that LHS ≠ RHS.
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There were 28 students in the RSM Math Challenge class. Over the year, eight students were late to class 12 times, 9 students were late 10 times, and the rest of the students were late
heeeeeeeelp
Answer:
3 students
Step-by-step explanation:
Now for RSM Olympiad are 8 math kangaroo are 7 studs that did both are 4
Total number of studs that participated are
(8-4) + 4 + (7-4)
4+4+3=11
those who didn't participate are
11-14-13
I'm quite confused on what I'm supposed to do here.
Hiya,
We literally just learnt about congruent shapes before the holidays.
I think it's like this-
If the shape is an SSS (Side, Side, Side) congruent or SAS (Side, Angle, Side), then you do the following:
a) Write the congruent statement... I'm not sure what the congruent statement is but it may be something you have learnt to do previously like an expression on revealing how to find the congruent shape and what type it is.
b) Sorry I'm not sure what a postulate is you may need to look back at your notes or research it.
I have attached images of the worksheet we were given in class which may or may not help!
Answer:
6. ΔANG ≅ ΔRWT by SAS Postulate.
7. The two triangles are congruent by SAS Postulate.
Step-by-step explanation:
Side-Angle-Side Postulate (SAS)If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.
Question 6The included angle is the angle between two sides of a triangle.
Therefore:
The included angle between AN and GN is angle N.The included angle between RW and TW is angle W.We are told that AN ≅ RW, GN ≅ TW, and ∠N ≅ ∠W.
Therefore, as two sides and the included angle in triangle ANG is congruent to the two sides and the included angle in triangle RWT, the SAS Postulate can be used to prove that the triangles are congruent.
Question 7The two given triangles have two sides of equal length, denoted by the same number of tick marks on each congruent line segment. The included angles are also congruent (both are 90°). Therefore, the SAS Postulate can be used to prove that the triangles are congruent.
4x−1<11 what is the answer
Answer:
Add 1 to both sides. Add 11 and 1 to get 12. Divide both sides by 4. Divide 12 by 4 to get 3.
"Susanna sells a lot for $45,400. She netted $41,428 after paying a broker’s commission. What was her rate of commission? (Hint: Before you find the rate of commission, you must find the amount of commission.)"
Alan invests $200 at a rate of per year compound interest. After 2 years the value of this investment is $206.46. Show that r²t 200r - 323=0
Answer:
unfortunately tdudeyiutddj try Zurich etu
PLEASE HELPPP DUE IN 2 HOURS!!!!!!!
Answer:
1.15%
Step-by-step explanation:
what is the formula for rectangle's perimeter
Step-by-step explanation:
the answer is 2(l+b) and it is verified
Solve: |x−5|>−2. Write your solution in interval notation.
(If there is no solution, enter your answer as ∅.)
Answer:
x ∈ R or (-∞,∞)
Step-by-step explanation:
The equation |x - 5| > -2 results in true for all x-values. No matter which x-values you substitute in the absolute value; positive, negative real numbers or zero, you'll always end up with the positive value which is greater than negative
Therefore, |x - 5| > -2 is true for all real x-values.
You have $319 of charges on your credit card. Then you charge $170 to buy Christmas presents. If your minimum payment if 6% of the balance, what will be your minimum payment?
Answer correctly and explain how you got the answer for brainliest.
Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = previous balance + new charge
Current balance = $319 + $170
Current balance = $489
The minimum payment is 6% of the current balance:
Minimum payment = 6% x current balance
Minimum payment = 6% x $489
Minimum payment = $29.34
Therefore, the minimum payment on the credit card would be $29.34.
Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = $319 + $170 = $489
Minimum payment = 6% x $489 = $29.34
The minimum payment on the credit card would be $29.34.
Hope this helped, have a GOOD DAY!!!!!
Find the area of the parallelogram.
Answer:
30 cm²
Step-by-step explanation:
The formula to find the area of a parallelogram.
Area = Base × Height
Accordingly, let us find the area.
Area = Base × Height
Area = 10 cm × 3 cm
Area = 30 cm²
There are 2 blueberries for every 7 strawberries. If there are 49 strawberries, how many blueberries are there?
Answer:
14
Step-by-step explanation:
So, 49 divided by 7 is 7 so there are 7 groups of 7 strawberries. With each of those 7 groups there are 2 blueberries. So, you are then going to multiply 7 by 2 and that gives you 14 blueberries.
T:R^3 to R^2 T(e1)=(1,4), T(e2)=(-2,9), T(e3)=(3,-8), where e1,e2, and e3 are the columns of the 3x3 identity matrix. Assume that T is a linear transformation. Find the standard matrix of T.
The value of standard matrix of T is,
⇒ [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Define T : R³ to R² as;
⇒ T(e₁) = (1, 4), T(e₂) = (-2,9), T(e₃) = (3,-8),
where e₁, e₂, and e₃ are the columns of the 3x3 identity matrix.
Now, The value of the standard matrix of T is,
T = [ T(e₁) T(e₂) T(e₃)]
= [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]
Therefore, The value of standard matrix of T is,
⇒ [tex]\left[\begin{array}{ccc}1&-2&3\\- 4&9&- 8\\\end{array}\right][/tex]
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Using repeated division method find the prime factors of 28
Answer:
Step-by-step explanation:
Finally, we got the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 28 are written as 2 × 2 × 7 or 22 x 7, where 2 and 7 are the prime numbers.
